Question

An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 56 cm. Find the area between the two consecutive ribs?

Answer 1

Hint: In the given question, we have been asked to find the area between the two consecutive ribs and it is given that an umbrella having 8 ribs which are equally spaced when assuming this to be a flat circle having radius equal to 56cm. To find the area between the two consecutive ribs, first we calculate the area of the circle then dividing the area by 8 and we will get the required answer.

Complete step by step solution:
We have given that,
An umbrella having 8 ribs.
Thus,
According to the question,
Area between the two consecutive ribs = \[\dfrac{1}{8} \times \text{area of the circle}\]
Now,
Area of the circle = \[\pi {{r}^{2}}\]
Here,
r = radius of the circle given = 56cm
Therefore,
Area of the circle = \[\dfrac{22}{7}\times {{\left( 56 \right)}^{2}}=\dfrac{22}{7}\times 56\times 56=9856\;c{{m}^{2}}\]
Area of the circle = \[9856\;c{{m}^{2}}\]
Now,
We have,
Area between the two consecutive ribs = \[\dfrac{1}{8}\times \text{area of the circle}\]
Therefore,
Area between two consecutive ribs = \[\dfrac{1}{8}\times 9856c{{m}^{2}}=1232\;c{{m}^{2}}\]
Hence, the area between the two consecutive ribs of the ribs is \[1232c{{m}^{2}}\] .
So, the correct answer is “ \[1232c{{m}^{2}}\] ”.

Note: In order to solve the question, students should remember the formula of calculating the area of the circle. They should be very careful while doing the calculation part to avoid making any error. Here to solve this question, we can use the alternative method that is first we assume the angle made by two consecutive ribs be \[\theta \] and we know that there are 8 numbers of equally spaced ribs and the complete angle of a circle is 360 degrees. So we find the angle made by 8 ribs by equating total angle ribs equals to 360 degrees and in this we can also find the required answer.